# What is the Mean Value Theorem for continuous functions?

If a function $f$ is continuous on $\left[a , b\right]$ and differentiable on $\left(a , b\right)$,
then there exists c in $\left(a , b\right)$ such that $f ' \left(c\right) = \frac{f \left(b\right) - f \left(a\right)}{b - a}$.